A318192 a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind.

1, 1, 5, 51, 781, 16005, 411881, 12776743, 464278585, 19350109449, 910126036909, 47694593157211, 2755988277318277, 174100457124362509, 11937317942278298961, 882942450221936166735, 70077737629245663437041, 5940877531422707027770385

Offset: 0

Author

Seiichi Manyama, Jan 07 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..352
• Wikipedia, Chebyshev polynomials.

Crossrefs

Cf. A323118.

Programs

PARI

{a(n) = polchebyshev(n, 2, n)/(n+1)}

PARI

{a(n) = sum(k=0, n\2, binomial(n, 2*k)*(n^2-1)^k*n^(n-2*k)/(2*k+1))}

Formula

a(n) = A323118(n)/(n+1).

a(n) = Sum_{k=0..floor(n/2)} (1/(2*k+1)) * binomial(n,2*k)*(n^2-1)^k*n^(n-2*k).